Persistence and stability of generalized ribosome flow models with time-varying transition rates

• Published in: PloS one Vol. 18; no. 7; p. e0288148
• Main Authors: Vághy, Mihály A, Szederkényi, Gábor
• Format: Journal Article
• Language: English
• Published: United States Public Library of Science 07.07.2023; Public Library of Science (PLoS)
• Subjects: Analysis; Biology and Life Sciences; Chemical reactions; Compartments; Computer and Information Sciences; Embedding; Entropy; Equilibrium; Flow stability; Health aspects; Kinetics; Liapunov functions; Messenger RNA; Modelling; Physical Sciences; Reaction Time; Ribosomes; Structural stability; Iran
• DOI: 10.1371/journal.pone.0288148
• ISSN: 1932-6203

In this paper some important qualitative dynamical properties of generalized ribosome flow models are studied. Ribosome flow models known from the literature are generalized by allowing an arbitrary directed network structure between compartments, and by assuming general time-varying rate functions corresponding to the transitions. Persistence of the dynamics is shown using the chemical reaction network (CRN) representation of the system where the state variables correspond to ribosome density and the amount of free space in the compartments. The L1 contractivity of solutions is also proved in the case of periodic reaction rates having the same period. Further we prove the stability of different compartmental structures including strongly connected ones with entropy-like logarithmic Lyapunov functions through embedding the model into a weakly reversible CRN with time-varying reaction rates in a reduced state space. Moreover, it is shown that different Lyapunov functions may be assigned to the same model depending on the non-unique factorization of the reaction rates. The results are illustrated through several examples with biological meaning including the classical ribosome flow model on a ring.